Question

A stock price is currently 100. Over each of the next to six months periods it is expected to go up by 10% or down by 10%. the risk free interest rate is 8% per annum. What is the value of the European call and put options with a strike price of 100? Verify that the put call parity is satisfied.

Answer 1

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Solution

As per given question

u = 1.1

d = .9

r = .08

δt = .5

T = 1, and K = 100.

So Risk neutral probability = e^r*t - d/(u-d)

p = e (.08)(.5) − (.9)/ 1.1 − .9 = .7041 and 1 − p = .2959.

The value of the call option is therefore f = e ^−(.08)(1)[(.7041)^2 (21)+(.7041)(.2959)(0)+(.2959)^2 )(0)] = $9.61.

value of put option = e ^−(.08)(1)[(.7041)^2 (0)+(.7041)(.2959)(1)+(.2959)^2 )(19)] = $ 1.92

For put call parity

Call option price + pv of strike price = put option price + spot price

LHS = 9.61 + 100*e^-.08 = 101.92

RHS = 1.92 + 100 = 101.92

hence proved